# Unitarity bounds on charged/neutral state mass ratio

## TL;DR

This paper derives unitarity bounds on the charge-to-mass ratio of particles in quantum gravity, revealing that extremely high ratios require additional light states, such as neutrinos, to maintain consistency.

## Contribution

It introduces a set of unitarity bounds on scattering amplitudes that constrain the spectrum of particles in quantum gravity theories.

## Key findings

- Light states with charge-to-mass ratio greater than 1 require neutral partners.
- Applied to the Standard Model, the bounds suggest the necessity of light neutrinos.
- Provides a new perspective on the spectrum constraints in quantum gravity.

## Abstract

In this letter, we study the implications of unitary completion of quantum gravity on the low energy spectrums, through an infinite set of unitarity bounds on the forward-limit scattering amplitudes. In three dimensions, we find that light states with charge-to-mass ratio $z$ greater than $1$ can only be consistent if there exists other light states, preferably neutral. Applied to the compactification of the Standard Model, where the low energy couplings are dominated by the electron with $|z|\sim 10^{22}$, this provides a novel understanding of the need for light neutrinos.